A direction-finding algorithm based on a reversed antenna array

Abstract

II. RECEIVED SIGNAL MODELwhere a(¢n)~ [1, e-j¢n, ... ,e-j(L-l)¢n]T is the direcThese code-multiplexed physical channels are mutually orthogonal; more details of the signal structure are provided in [12], though they are not needed here to describe the DOA estimator. The received signals x(k) ~[xl(k), ... , xL(k)]T from N different base stations impinge on an L-element ULA, yielding(1) N x(k) == L a(¢n)s(n)(k) + n(k) n=l Although we consider the signal format of wideband CDMA (WCDMA) because pilot signals are available to train the beamformer, the reversed beamformer can be applied to other systems. Moreover, it is shown in [11] that the reversed array can also be used for blind direction finding, i.e., without a training signal.In the WCDMA downlink, let s(n) (k) denote the transmitted signal from the nth base station at time instant k. It consists of the common pilot channel (CPICH) s~n)(k) and M user traffic channels, which can be written in baseband form asThe DOA estimation technique presented here is also based on estimating a phase difference, but unlike the subarray approach, it exploits the phase difference between the output of a conventional beamformer and that of a reversed beamformer [8] with the same number of antenna signals. As a result, a more accurate DOA estimate is obtained while maintaining a complexity similar to that of the subarray approach. Although reversing the antenna signals has some similarity with forwardbackward averaging techniques and algorithms for centrosymmetric arrays [4], [9], [10], the approach here exploits phase differences rather than the properties of the received signal correlation matrix or subspaces. The phase estimate obtained using the reversed beamformer is an integer multiple of the unknown phase of the signal of interest, so that when dividing by this integer, the corresponding noise variance is reduced compared to the subarray approach.

Blind phase-shift-based DOA estimation

“…Using the notation in [2], the output of the first subarray is y(k), and the output of the second subarray is denoted by y s (k) = w H o x s (k) where the beamformer weight vector is of size L − 1, and x s (k) [x 2 (k), . .…”

“…With the aid of a pilot signal, it is shown in [1] that the subarray improves the performance of conventional DOA estimators, such as the multiple signal classification (MUSIC) [3] algorithm and estimation of signal parameters via rotational invariance techniques (ESPRIT) [4]. It is shown in [2] that the reversed beamformer has better performance than the overlapping subarrays because of the following properties: (i) it uses the full antenna array and thus can suppress more cochannel interference, and (ii) the phase difference in the reversed array is an integer multiple of the unknown phase of the signal of interest. In this paper, we investigate the performance of a reversed beamformer for blind applications where a training signal is not available for use in phase-shift-based DOA estimation.…”

“…The beamformers can be implemented using overlapping subarrays as described in [1], or they can be a conventional beamformer and the reversed array in [2] where the antenna signals of the second beamformer are in reverse position. These lowcomplexity techniques can have a high resolution because the DOA estimate is computed at the output of the beamformers where the cochannel interference has been suppressed and the noise power has been reduced.…”